Learn About the Associative Property in Math

Learn About the Associative Property in Math According to the associative property, the addition or multiplication of a set of numbers is the same regardless of how the numbers are grouped. The associative property will involve 3 or more numbers. The parenthesis indicates the terms that are considered one unit. The groupings (Associative Property) are within the parenthesis. Hence, the numbers are associated together. In multiplication, the product is always the same regardless of their grouping. The Associative Property is pretty basic to computational strategies. Remember, the groupings in the brackets are always done first, this is part of the order of operations. Addition Example of the Associative Property When we change the groupings of addends, the sum does not change:(2 5) 4 11 or 2 (5 4) 11(9 3) 4 16 or 9 (3 4) 16Just remember that when the grouping of addends changes, the sum remains the same. Multiplication Example of the Associative Property When we change the groupings of factors, the product does not change:(3 x 2) x 4 24 or 3 x (2 x 4) 24.Just remember that when the grouping of factors changes, the product remains the same. Think Grouping! Changing the grouping of addends does not change the sum, changing the groupings of factors, does not change the product. Simply put, regardless of whether you show 3 x 4 or 4 x 3, the final result is the same. In addition, 4 3 or 3 4, you know that the outcome is the same, the answer remains the same. However, this is NOT the case in subtraction or division so when you think of the associative property, remember that the final result or answer remains the same or its not the associative property. The understanding of the concept of associative property is much more important that the actual term associative property. Titles often confuse students and youll discover that youll ask what the associative property is, only to be returned with a blank look. However, if you say to a child something like If I change the numbers in my addition sentence, does it matter? In other words, can I say 5 3 and 3 5, will the child that understands say yes because its the same? When you ask if you can do this with subtraction, theyll laugh or tell you that you cant do that. So in essence, a child knows about the associative property which is really all that matters even though you may stump them when you ask for a definition of the associative property. Do I care that the definition escapes them? Not at all, if they indeed know the concept. Lets not trip our students up with labels and definitions when concept understanding is the key ingredient in math.

Proportions Problems Worksheet - Practical Questions

Proportions Problems Worksheet - Practical Questions A proportion is a set of 2 fractions that equal each other. This article focuses on how to use proportions to solve real life problems. Real World Uses of Proportions Modifying a budget for a restaurant chain that is expanding from 3 locations to 20 locationsCreating a skyscraper from blueprintsCalculating tips, commissions, and sales tax Modifying a Recipe On Monday, you are cooking enough white rice to serve exactly 3 people. The recipe calls for 2 cups of water and 1 cup of dry rice. On Sunday, you are going to serve rice to 12 people. How would the recipe change? If you’ve ever made rice, you know that this ratio - 1 part dry rice and 2 parts water  - is important. Mess it up, and you’ll be scooping a gummy, hot mess on top of your guests crawfish à ©touffà ©e. Because you are quadrupling your guest list (3 people * 4 12 people), you must quadruple your recipe. Cook 8 cups of water and 4 cups of dry rice. These shifts in a recipe demonstrate the heart of proportions: use a ratio to accommodate lifes greater and smaller changes. Algebra and Proportions 1 Sure, with the right numbers, you can forgo setting up an algebraic equation to determine the amounts of dry rice and water. What happens when the numbers are not so friendly? On Thanksgiving, youll be serving rice to 25 people. How much water   do you need?Because the ratio of 2 parts water and 1 part dry rice applies to cooking 25 servings of rice, use a proportion to determine the quantity of ingredients. Note: Translating a word problem into an equation is super important. Yes, you can solve an incorrectly set up equation and find an answer. You can also mix rice and water together to create food to serve at Thanksgiving. Whether the answer or food is palatable depends on the equation. Think about what you know: 3 servings of cooked rice 2 cups of water; 1 cup of dry rice25 servings of cooked rice ? cups of water; ? cup of dry rice3 servings of cooked rice/25 servings of cooked rice 2 cups of water/x cups of water3/25 2/x Cross multiply. Hint: Write these fractions vertically to get the full understanding of cross multiplying. To cross multiply, take the first fractions numerator and multiply it by the second fractions denominator. Then take the second fractions numerator and multiply it by the first fractions denominator.3 * x 2 * 253x 50Divide both sides of the equation by 3 to solve for x.3x/3 50/3x 16.6667 cups of waterFreeze- verify that the answer is correct.Is 3/25 2/16.6667?3/25 .122/16.6667 .12Whoo hoo! The first proportion is right.   Algebra and Proportions 2 Remember that x will not always be in the numerator. Sometimes the variable is in the denominator, but the process is the same. Solve the following for x. 36/x 108/12 Cross multiply:36 * 12 108 * x432 108xDivide both sides by 108 to solve for x.432/108 108x/1084 xCheck and make sure the answer is right. Remember, a proportion is defined as 2 equivalent fractions:Does 36/4 108/12?36/4 9108/12 9It’s right! Practice Exercises Instructions: For each exercise, set up a proportion and solve. Check each answer.1. Damian is making brownies to serve at the family picnic. If the recipe calls for 2  ½ cups of cocoa to serve 4 people, how many cups will he need if there will be 60 people at the picnic? 2. A piglet can gain 3 pounds in 36 hours. If this rate continues, the pig will reach 18 pounds in _________ hours. 3. Denise’s rabbit can eat 70 pounds of food in 80 days. How long will it take the rabbit to eat 87.5 pounds? 4. Jessica drives 130 miles every two hours. If this rate continues, how long will it take her to drive 1,000 miles?

Chemistry Major College Courses

Chemistry Major College Courses Are you interested in studying chemistry in college? Here is a look at the courses you can expect to take if you have a chemistry major. The specific courses you take will depend on which school you attend, but in general you can expect a heavy emphasis on chemistry and math. Almost all of the chemistry courses include a lab component, too. General ChemistryOrganic ChemistryInorganic ChemistryBiochemistryAnalytical ChemistryPhysical ChemistryPhysicsBiologyCalculusProbabilityStatistics Computer Science Sequence of Courses Some of the required classes can be taken whenever you can fit them into your schedule, such as probability, statistics, and computer science. Others have prerequisites. What this means is that you have to take one or more other classes before youll be allowed to enroll. If possible, a chemistry major should try to take general chemistry as a freshman. The course is typically broken up into two parts and takes an entire academic year to complete. Taking it early helps a student determine whether chemistry is truly what they want to pursue and it opens the opportunity to take organic chemistry. Organic chemistry also requires an entire academic year to complete at most institutions. It is a prerequisite for biochemistry and other interdisciplinary courses. In other words, a student usually needs three years to get through the general chemistry, organic chemistry, and biochemistry sequence. If youre a chemistry major and you wait until your junior (third) year to take general chemistry, you cant graduate in less than four and a half years! In addition to organic chemistry, general biology is a prerequisite for biochemistry. General biology lasts an entire academic year. A student should be careful when registering for general biology to make certain its the correct class. Many schools offer a watered down version of general biology for non-science majors that may count for college credit, but wont satisfy the requirements for a major or to take higher level biology or chemistry courses. Physics and sometimes calculus are required to take physical chemistry. Because physics is often taken in the second or third year, its normal for physical chemistry to be one of the last major courses a chemistry major takes. Inorganic chemistry always requires general chemistry. Some schools tack on additional requirements. Like physical chemistry, its typically taken later in a students academic career.

The Irish Potato Famine Essay Example | Topics and Well Written Essays - 1500 words

The Irish Potato Famine - Essay Example Let us try to overview the historical context which preceded The Irish Potato Famine, and on ground of this try to find out what principle factors provoked the famine. The Irish Potato Famine is the name of a famine that took place in Ireland between 1845 and 1849, but immediate effects of which were felt until 1851. If we refer to dry statistics, then we may learn that the total number of people who died from this famine is unclear because there were no exact historical records. However, according to different estimates it is supposed that the general number of victims that can be directly and indirectly attributed to the famine ranges from 500,000 to more than one million (Lyons, 1985, p.14). Aside from the enormous death toll, there were many other social and economic consequences of the famine. Among such consequences were several million Irish refugees who during and after the famine emigrated to Britain, America, Canada, and Australia (Scally, 1996, p.167). Also, as we shall see, the effects of the famine on Irish culture and economy were so great that it significantly changed them. At this point we may begin to wonder whether the very fact that such a profound historical event as the Irish Potato Famine took place can be explained purely by natural causes, or maybe there was an involvement of social, economic, and political factors which contributed to the famine To see if this was the case, let us firstly overview political and economic environment in which the famine happened, and then consider demographic and agricultural aspects relevant to the famine. Speaking of the political context of the famine, we of course must mention relations between Ireland and Great Britain in the middle of the nineteenth century. Since the Act of Union of 1800 Ireland was to be formally represented by one hundred members in the House of Commons in the United Kingdom, which was merely a one-fifth proportion of representation of Great Britain. Moreover, in addition to the low level of Irish representation in the parliament of Britain the needs of Ireland were given a low priority. It was not surprising as most of the members of government had never even been in Ireland themselves. To better feel the situation of that time, we should add that the British dominance was as well fortified by the unification of the churches of Ireland and England, with the ensuing leadership in Ireland of the Anglicans and exclusion of Roman Catholics and Presbyterians from membership in governmental bodies. Only by 1829 was political equality restored in Ireland in certain s pheres. This included the possibility to participate in free trade between the British Isles, and admission of Irish merchandise to colonies of Britain on equal terms with British goods (Otuathaigh, 1972). Now, on ground of the mentioned signs of oppression of Ireland it was suggested by some historians that the Irish Potato Famine was in fact a genocide initiated by the British against Ireland. However, this accusation is dismissed by most scholars as too radical, and instead it is thought that the policies of Britain during the famine can rather be blamed as fallacious, ignorant, and fatal, and that as a significant reduction of population of Ireland was deemed desirable by many British politicians they might just had decided not to intervene in the natural course

Personal and Professional Development Essay Example | Topics and Well Written Essays - 2000 words

Personal and Professional Development - Essay Example Professional engineering qualifications at various levels are discussed below: Vocational A-Levels and Scottish Highers; SQA Higher National Certificate: These are courses for 1 or 2 years full time. These courses can be regarded as foundation qualifications for the engineering technicians and can be utilised to get admission in undergraduate studies. BTEC/Edexcel/SQA Higher National Diploma (HND): These are generally 2 years course, full time. The HND is well respected qualification and can help the student to upgrade as an Incorporated Engineer (IEng). By obtaining better marks, one can also get transferred into the 2nd or 3rd year of an undergraduate degree programme. Degree Courses: These courses include BEng (Hons) (Bachelor of Engineering) or MEng (Master of Engineering). A BEng (Hons) would generally take 3 to 4 years full time to complete. An accredited professional Bachelor’s degree would fulfil the educational requirements for registration at the level of Incorporate d Engineer (IEng). This sort of degrees as per the specifications of the Engineering Council must last at least 3 years full time. The MEng can be regarded as an integrated form of Master’s degree. It is a higher qualification than BEng (Hons). It takes 4 to 5 years full time to complete. An accredited professional MEng would fulfil the academic requirements for the Chartered Engineer (CEng) qualification. This level of engineering qualification is the best in the educational world of UK and is highly respected all across the industries. An accredited professional BEng (Hons) degree together with a suitable Master’s degree or appropriate extended learning to the Master’s level would also meet the educational requirements.... This paper stresses that the professional titles which are awarded by the Engineering Council are well protected by the law. Registration in Engineering Council by different engineers and technicians is voluntary. This report makes a conclusion that engineering is a challenging profession in the modern work environment. Globalisation requires the engineers to be competent and skilled at the global standards. United Kingdom needs a powerful army of engineers and technicians to combat recession and obtain economic growth. Therefore, the routes to personal professional accreditation in engineering are not easy. The authortThe candidates have to be sufficiently skilled, competent and up to the minute to become a professionally qualified engineer as per the UK standards. No doubt that pursuing a degree course like BEng or MEng is the best way to obtain in depth knowledge in the field and become a professionally qualified engineer. BEng and MEng programmes in civil and structural engineering provided by the UK universities cater to the global standards in this context. Else, if a student cannot pursue a university program for some reason, he can appear in the examinations conducted by the Engineerin g Council and progress through the Level 5, Level 6 and Level 7 qualifications in a step by step manner. An engineer must possess numerical ability, analytical skill, creativity, and most importantly, engineering aptitude to obtain the different engineering qualifications discussed so far and excel in the engineering field. An engineering qualification can serve as both a basic qualification and a specialised qualification, and thus it can open up several prospects.

Comparison of PICASSO, Gertrude Stein and GAUGUIN, Two Tahitian Women Term Paper

Comparison of PICASSO, Gertrude Stein and GAUGUIN, Two Tahitian Women - Term Paper Example The work of Gauguin involves the use of several elements in painting that are similar to other post-impressionists. In Two Tahitian Women, Gauguin uses simplified colors and solid form to come up with the painting. Building from flat objects lacking traditional notions of perspective, Gauguin presents his ideas perfectly in the painting. The use of a white table cloth pushed directly to the foreground of the picture creates the still-life concept developed by Gauguin. The painting uses soft golden hues in the treatment of light with the focus being on primitivism and uses nude picture. (Eaves 89) The question asked by the observer is whether the approach of Gauguin is to present evil or immorality to the children. In fact, the challenge is with the views especially with the treatment of breast in the picture. The presentation of seminude women in the painting is a source of concern for the society.  Analysis of the work of Gauguin However, the artistic impression presente d is superb because it combines all the elements of painting to form a striking picture. The picture is not a deliberate attempt towards eroticism because the soft shadows on the woman’s breast contribute to their beauty, by capturing all sense of femininity using the light aesthetically. The reproduction of the paintings has added the use of the terms mango blossoms which is not on the original painting. The use of light in the picture is excellent because it brings out the integral elements in the picture, which is femininity and emotional attraction. The work by Gauguin presents his personal opinion and idea about feminism and the role of women in the society (Barnet 63). The artistic presentation of semi-nude women brings out the focus of the artist in the society. It involves personal opinion, but the postmodernism presents the various ideas as a social issue that affected most of the artist. Post-impressionism in the artistic presentation of the 1900s is by the envir onment of the artists. Gauguin developed his own style by using vivid and bold colors, which does not show a naturalistic bias. He does not use a visible outlining in the painting but emphasizes the shapes of nature without basic outline.  The forms presented are more decorative and separate forms rather than presenting the idea as a cohesive and natural landscape. His synthetic style is not evident, but there are particular features associated with synthetic style. It is that the change in style may be a product of influence from his friend Emile Bernard especially his painting of Breton women (Eaves 124). The influence of other artists on the work of Gauguin is evident in the artwork done during their friendship. For example, the Old Women at Arles unites the influence of Bernard and Van Gogh illustrating the similarity in style between the two artists.  Analysis of the paintings of Picasso The work of Picasso is different from Gauguin because Picasso focused his work ed on the social issues. Picasso’s most common work was Guernica, which is a powerful political statement. The work of Picasso focused on his emotions in relation to events in the society. Picasso was against attack by Spain on the civilian. The invasion spearheaded the work of Picasso who devoted himself in using art to denounce the evils of the intentional military intrusion and attack on civilians. The work of art by Picasso

Information systems management Assignment Example | Topics and Well Written Essays - 750 words

Information systems management - Assignment Example Assessment of the firm’s mission for information systems management The mission for the firm’s information systems management is to support the teaching and administrative purposes of the university in an efficient way. Olsen offers a criterion for assessing the mission based on the perspective of an effective mission statement. One of the author’s offered based for analysis is the mission’s point of focus and he argues that a good and effective mission focuses on meeting customers’ needs instead of an organization’s interest in its products. Even though the university’s information systems management is framed to focus on a product, teaching and administration, these leads to a conducive and quality learning that meets the needs and expectations of students and other stakeholders in the education sector. Empowering teaching and administration of learning processes also identifies competence intent of the mission statement and hence it s quality. The mission also focuses on teaching staff and motivates them through support to their scope of work. Further, the mission is clear and can be understood from its simple phrase is achievable, â€Å"specific, short, sharply focused, and memorable† (Olsen, 2011, p. 94). These standards therefore qualify the mission statement. Assessment of the firm’s goals Analysis of the university’s information systems management goals also identifies effectiveness of the set goals towards meeting the department’s objectives. Based on the SMART features criteria for good goals, the goals should be â€Å"specific, measurable, attainable, relevant, and time oriented† (Cassidy and Kreitner, 2009, p. 69). The organizations goals are being at the start of the art in course delivery at a distance, providing 24x7 reliability in WebTycho, Desire2Learn, PeopleSoft and other essential UMUC information systems, and conserving State and student (ie, tuition) resourc es in accomplishing the foregoing. The goals are simple to understand because of their precise scopes and can be quantified for evaluation of success. Being at the start of art is measurable from comparison with competing institutions while the conservation goal can be determined from resource utility and sustainability. Analysis of the goals also identifies attainability under resource availability, relevance of the academic scope of the institution, and can be achieved in a set period. They are therefore good goals for pursuit (Cassidy and Kreitner, 2009). Importance of information systems management in the firm Information systems management plays a major role in meeting informational needs of stakeholders, mainly students, administration, and teachers. As an academic institution, the university supports students and teachers through availing required academic resources in technology based forms such as online library and inform the administration of efficiency with which the sta keholders’ needs are met and of needs for improvement of services that relates to information system (Asemi, Safari and Zavareh, 2011). The department, in its management capacity, offers leadership and liaison roles, monitor and evaluates processes, facilitates informed decisions in the institution through collection, analysis and dissemination of data (Bagad, 2009).